Well, somebody decided to practice TEH SCIENTISMZ! and see if that hypothesis holds for influenza.
Researchers went to dozens of Hutterite communities in Canada, and vaccinated children for influenza in some, but not others (on average, in the vaccinated communities, 83% of children received the vaccine; in unvaccinated, it was 12%). Here’s what they found:

Laboratory-confirmed influenza was detected in 119 nonrecipients: 39 (3.1%) in the colonies assigned to influenza immunization (23, influenza A and 16, influenza B by RT-PCR) and 80 (7.6%; 60, influenza A and 20 influenza B by PCR) in colonies assigned to hepatitis A. The level of indirect vaccine protectiveness was 61% (95% CI, 8%-83%; P = .03) in an adjusted model.

If you didn’t receive the vaccine, your chance of getting influenza dropped 61% if you lived in a community with heavily vaccinated children. Keep in mind that the rest of the community really wasn’t vaccinated (only 12% were vaccinated, other than study children). If the adults had been vaccinated too, the overall rate would have dropped further (if for no other reason, some of the infected adults would have been immune, never mind that they would also have been unable to infect other people themselves).

Vaccination is an incredibly effective intervention, despite what woomeisters and other sundry fucking morons might have you believe. It is time we adopt a national influenza vaccination policy that uses schools to vaccinate children (with an opt-out option), along with targeting high-contact adults (e.g., medical personnel, teachers, police officers).

We would save thousands of lives every year, and we don’t have to march, skip, run, jump, or pogo stick for a cure. We just have to vaccinate.